Simple, Fast, and Flexible Framework for Matrix Completion with Infinite Width Neural Networks

TL;DR

This paper introduces a simple, fast, and flexible infinite-width neural network framework for matrix completion, leveraging neural tangent kernels to improve computational efficiency and incorporate prior knowledge.

Contribution

It develops an infinite-width neural network approach for matrix completion using neural tangent kernels, enabling efficient, flexible, and semi-supervised learning capabilities.

Findings

Competitive results in drug screening and image inpainting

Derivation of neural tangent kernels for various network architectures

Accessible Python implementation for standard hardware

Abstract

Matrix completion problems arise in many applications including recommendation systems, computer vision, and genomics. Increasingly larger neural networks have been successful in many of these applications, but at considerable computational costs. Remarkably, taking the width of a neural network to infinity allows for improved computational performance. In this work, we develop an infinite width neural network framework for matrix completion that is simple, fast, and flexible. Simplicity and speed come from the connection between the infinite width limit of neural networks and kernels known as neural tangent kernels (NTK). In particular, we derive the NTK for fully connected and convolutional neural networks for matrix completion. The flexibility stems from a feature prior, which allows encoding relationships between coordinates of the target matrix, akin to semi-supervised learning. The effectiveness of our framework is demonstrated through competitive results for virtual drug screening and image inpainting/reconstruction. We also provide an implementation in Python to make our framework accessible on standard hardware to a broad audience.